Offset and slotted-lever mechanisms can produce unequal input-angle intervals for opposite strokes. This calculator evaluates a narrow ideal angle construction from an entered offset and radius; it does not solve a complete reciprocating linkage.
Variable Reciprocating Motion Interactive Calculator
Enter an offset smaller than the entered radius. Results are an ideal angular comparison—not slider travel, connecting-rod kinematics, stroke time under varying speed, force or machine capacity.
Equation Used
- Offset and radius are positive entered lengths with e<r.
- The construction angle is beta=asin(e/r).
- The two reported sweeps are defined as 180 degrees plus and minus beta.
- Input angular speed is treated as uniform only when interpreting sweep ratio as an ideal time ratio.
- Connecting-rod length, slider displacement, dead-center geometry, velocity, acceleration, force, torque, friction, compliance, stress, wear and safety are omitted.
Documented Unequal-Stroke-Angle Topology
U.S. Patent 479,742 describes a quick-return slit-bar motion in which an offset between shaft centers makes a uniformly driven pin move a slotted bar through unequal portions of the cycle. NASA mechanism reports separately document crank-slider and offset quick-return mechanisms.
The animation illustrates offset centers and a slotted lever. Its numeric outputs use the angle construction below; they do not establish the stroke endpoints of a complete linkage.
What This Calculator Represents
The tool normalizes the entered offset by the entered radius, takes the inverse sine, forms two complementary sweeps around 180 degrees and divides one by the other.
Ideal Offset-radius Sweep Comparison
construction angle beta = asin(q)
defined sweep A = 180 deg + beta
defined sweep B = 180 deg - beta
ideal sweep ratio = sweep A / sweep B
Under an additional assumption of constant input angular speed, this angular ratio is also an ideal elapsed-time ratio for the two defined intervals.
Worked Arithmetic Example
For entered offset 60 mm and radius 70 mm, q=0.8571 and beta is about 59.0 degrees. The defined sweeps are about 239.0 degrees and 121.0 degrees, giving an ideal sweep ratio of about 1.98:1.
Model Boundary
- Calculated: one inverse-sine construction angle, two defined sweeps and their ratio.
- Illustrated: a generic offset-center slotted-lever cue.
- Not calculated: complete offset slider-crank or Whitworth geometry, slider travel, actual dead centers, speed variation, acceleration, force, stress, wear, capacity or safety.
Frequently Asked Questions
Is this a complete slider-crank solution?
No.
Why is connecting-rod length absent?
Because the model is only an offset-radius angle construction.
Does sweep ratio always equal a machine's time ratio?
Only under the stated constant-input-speed interpretation and matching interval definition.
Are slider displacement and stroke calculated?
No.
Are forces or loads calculated?
No.
Can this size a quick-return machine?
No.
References
- U.S. Patent 479,742, Conveyer and screen: quick-return slit-bar motion with offset shaft centers and a uniformly driven crank pin.
- NASA mechanism report: four-bar, offset slider-crank and offset quick-return mechanisms.
- NASA report with dimensioned crank-slider geometry including crank, connecting rod and offset.
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